49 research outputs found
Intrinsic and emergent anomalies at deconfined critical points
It is well known that theorems of Lieb-Schultz-Mattis type prohibit the
existence of a trivial symmetric gapped ground state in certain systems
possessing a combination of internal and lattice symmetries. In the continuum
description of such systems the Lieb-Schultz-Mattis theorem is manifested in
the form of a quantum anomaly afflicting the symmetry. We demonstrate this
phenomenon in the context of the deconfined critical point between a Neel state
and a valence bond solid in an square lattice antiferromagnet, and
compare it to the case of honeycomb lattice where no anomaly is
present. We also point out that new anomalies, unrelated to the microscopic
Lieb-Schultz-Mattis theorem, can emerge prohibiting the existence of a trivial
gapped state in the immediate vicinity of critical points or phases. For
instance, no translationally invariant weak perturbation of the
gapless spin chain can open up a trivial gap even if the spin-rotation symmetry
is explicitly broken. The same result holds for the deconfined
critical point on a square lattice.Comment: 25 pages + Appendice
Instabilities near the onset of spin density wave order in metals
We discuss the low energy theory of two-dimensional metals near the onset of
spin density wave order. It is well known that such a metal has a
superconducting instability induced by the formation of spin-singlet pairs of
electrons, with the pairing amplitude changing sign between regions of the
Fermi surface connected by the spin density wave ordering wavevector. Here we
review recent arguments that there is an additional instability which is nearly
as strong: towards the onset of a modulated bond order which is locally an
Ising-nematic order. This new instability is a consequence of an emergent
"pseudospin" symmetry of the low energy theory---the symmetry maps the
sign-changing pairing amplitude to the bond order parameter.Comment: 14 pages, 9 figures; contribution to the special issue of the New
Journal of Physics on "Fermiology of Cuprates", edited by Mike Norman and
Cyril Prous
Wilson Loops in Non-Compact U(1) Gauge Theories at Criticality
We study the properties of Wilson loops in three dimensional non-compact U(1)
gauge theories with global abelian symmetries. We use duality in the continuum
and on the lattice, to argue that close to the critical point between the Higgs
and Coulomb phases, all correlators of the Wilson loops are periodic functions
of the Wilson loop charge, Q. The period depends on the global symmetry of the
theory, which determines the magnetic flux carried by the dual particles. For
single flavour scalar electrodynamics, the emergent period is Q = 1. In the
general case of N complex scalars with a U(1)^{N-1} global symmetry, the period
is Q = N. We also give some arguments why this phenomenon does not generalize
to theories with a full non-abelian SU(N) symmetry, where no periodicity in Q
is expected. Implications for lattice simulations, as well as for physical
systems, such as easy plane antiferromagnets and disordered superfluids, are
noted.Comment: 25 pages, 1 figur
Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order
We present a renormalization group theory for the onset of Ising-nematic
order in a Fermi liquid in two spatial dimensions. This is a quantum phase
transition, driven by electron interactions, which spontaneously reduces the
point-group symmetry from square to rectangular. The critical point is
described by an infinite set of 2+1 dimensional local field theories, labeled
by points on the Fermi surface. Each field theory contains a real scalar field
representing the Ising order parameter, and fermionic fields representing a
time-reversed pair of patches on the Fermi surface. We demonstrate that the
field theories obey compatibility constraints required by our redundant
representation of the underlying degrees of freedom. Scaling forms for the
response functions are proposed, and supported by computations by up to three
loops. Extensions of our results to other transitions of two-dimensional Fermi
liquids with broken point-group and/or time-reversal symmetry are noted. Our
results extend also to the problem of a Fermi surface coupled to a U(1) gauge
field.Comment: 46 pages, 11 figures; paper II is arXiv:1005.1288 ; (v3) added
results for off-critical behavior; (v4+v5) added clarifications, including
new appendi
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Valence Bond Solid Order Near Impurities in Two-Dimensional Quantum Antiferromagnets
Recent scanning tunneling microscopy (STM) experiments on underdoped cuprates have displayed modulations in the local electronic density of states, which are centered on a Cu-O-Cu bond [Kohsaka et al. Science 315 1380 (2007)]. As a paradigm of the pinning of such bond-centered ordering in strongly correlated systems, we present the theory of valence bond solid (VBS) correlations near a single impurity in a square lattice antiferromagnet. The antiferromagnet is assumed to be in the vicinity of a quantum transition from a magnetically ordered Néel state to a spin-gap state with long-range VBS order. We identify two distinct classes of impurities: (i) local modulation in the exchange constants and (ii) a missing or additional spin, for which the impurity perturbation is represented by an uncompensated Berry phase. The “boundary” critical theory for these classes is developed. In the second class, we find a VBS pinwheel around the impurity, accompanied by a suppression in the VBS susceptibility. Implications for numerical studies of quantum antiferromagnets and for STM experiments on the cuprates are noted.Physic